Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [arithmetic]

Questions on basic arithmetic involving numerical quantities only. Questions involving variable values (other than the result of the operation) should be placed under the (algebra-precalculus) tag. Questions about number theory (sometimes called "arithmetic") should not use this tag and should instead use (number-theory) or (elementary-number-theory).

Arithmetic is defined as operations upon numbers using $4$ main operations along with many others:

addition - the sum of two numbers

subtraction - the difference of two numbers also defined as the addition of negative numbers

multiplication - the area of a rectangle with sides of lengths equal to the two operands

division - the number of times one number can be subtracted from another before equaling zero. Sometimes it will allow decimals and in other cases there will be a remainder left over when a number doesn't go into another evenly

See Arithmetic.

6283 questions
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Expressions $x^a+1$ and $x^b+1$, when $a$, $b$ are odd positive integers

Let $a\geq 3$ and $b\geq 3$ be odd integers. Let $x\geq 2$ be an integer. I would like to know if we can state that $x^a+1|x^b+1 \Longleftrightarrow a|b$. I know how to prove that $a|b$ implies $x^a+1|x^b+1$. Is the other implication also true? I'm…
Alchimist
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$1+1+1+1+1+1+1+1+1+1+1+1 \cdot 0+1 = 12$ or $1$?

Does the expression $1+1+1+1+1+1+1+1+1+1+1+1 \cdot 0+1$ equal $1$ or $12$ ? I thought it would be 12 this as per pemdas rule: $$(1+1+1+1+1+1+1+1+1+1+1+1)\cdot (0+1) = 12 \cdot 1 = 12$$ Wanted to confirm the right answer from you guys. Thanks for…
Dev01
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Pigeonhole principle applied in an arithmetic problem

Choose $a_1,a_2,\dots,a_{50}$ from the set $\{1,2,3,\dots,98\}$ at random. Denote by $A$ the set that contains the chosen numbers. State, with arguments, if the followings assertion are true or false. a) There exists two numbers in $A$ such that…
stefano
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Are there any integers a and b such that $a^2+b^2 = 10^{100}+3$

I try to find integers $a$ and $b$ such that $a^2+b^2 = 10^{100}+3$, I try some number without any result
Fouad El
  • 371
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why is -1 mod 3 = 2?

Title says it all. Google doesn't have anything. Trying to get it to let me submit by typing more words. There is nothing really to be added but it wont let me submit without this.
sabertenn
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Multiplying two numbers is the average squared minus sum of odd numbers of k equal average minus smallest number. Why?

Multiplying two numbers is the average squared minus sum of odd numbers k equal average minus smallest number. Why is that happening? What is the logic behind it? It is puzzling me. For example (examples only for numbers that give integer averages,…
Lucian Viorel
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Operations and fungibility of units

From the commutative property of the reals, we have that: $$ x+y=y+x $$ In other words, the order of items does not matter, just their overall quantity when determining the sum. Imagine I have \$5. Here, $ 1+1+1+1+1=5 $. I can re-arrange the $1's$…
Kwame Brown
  • 283
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Arithmetic question- invariance of objects involved

I have an exceedingly simple question, but something that has been eating at me for some time now. Imagine that we wish to perform subtraction of objects with the same units, say \$. I have a total of 10\$, composed of 5\$ of my own money, and 5\$…
Kwame Brown
  • 283
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How to calculate the growth when old number is negative?

Sorry, I feel like an idiot for not knowing this, but assume my old number is -10. How would I calculate a 50% growth of that -10? Multiplying -10 by 1.50 results in -15 which is going in the wrong direction. But multiplying 1.50 with the absolute…
sudden_clarity_clarence
  • 101
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Don't know how to solve a question regarding sets

The next definition is giving in the book the exercise was proposed on. The definition reads: Let $a=n(A)$ and $b=n(B)$ where $A$ and $B$ are two disjoint finite sets. Then $a+b=n(A∪B).$ I understand the fact of A and B being disjoint is a must.…
ceip7bavSi ceip7bavSi
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Basic maths question

If I have 25 apples and multiply them zero times, why is it that I end up with zero? I understand zero times means no times, right? I mean, multiply by zero is no multiplication. Can anyone explain, please?
Claudio Elgueta
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4 equations with specific set of numbers

I must make 1 addition (x+y=z), 1 subtraction (x-y=z), 1 multiplication (x*y=z), and 1 division (x/y=z) equation with the following numbers. All the numbers must be used to fill x, y, and z of each equation. x, y, and z can consist be 1, 2, or…
GiantDuck
  • 129
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For $x\neq 1$ find $x$ such that ...

For $x\neq 1$, find $X$ such that: $$x+1\mid 2$$ $$x+2\mid 3$$ $$x+3\mid 4$$ $$x+4\mid 5$$ Can someone help me with this ?
medamin
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Show that $n^4+4$ is a composite number

Show that if $n>1$, then the number $z=n^4+4$ is a composite number. I only tried to analyze the parity of the number $n$: if $n$ is even then $z$ is even; if $n$ is odd then $z$ is odd. But the second part didn't help me much, how can I…
sant
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Nth digit of k!

Is there any way to know the nth digit of k! without having to calculate the factorial? And, for some k, when k! is prime? (disregarding the trailing zeros, and k>2)
thiago
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